Abstract
It is shown how the trace and the determinant of an operator can vary with the algebra which contains the operator. The main conclusion is that if the operator is not of trace class, then generally speaking, the values of the trace constitute the whole complex plane and the values of the determinant are either a singleton {0} or the set C\{0}.
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© 2000 Springer Basel AG
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Gohberg, I., Goldberg, S., Krupnik, N. (2000). Possible Values of Traces and Determinants. Perelson Algebras. In: Traces and Determinants of Linear Operators. Operator Theory Advances and Applications, vol 116. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8401-3_8
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DOI: https://doi.org/10.1007/978-3-0348-8401-3_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9551-4
Online ISBN: 978-3-0348-8401-3
eBook Packages: Springer Book Archive